LCA Maths Department

Transcription

1 Name: LCA Maths Department Unit 19 Higher Check-in test 1 Calculator Q1. Complete the table of values for 6 y x x y Q2. On the grid, draw the graph of 6 y for 0. x x

2 Q3. The graph of y = f(x) is transformed to give the graph of y = f(x + 3) The point A on the graph of y = f(x) is mapped to the point P on the graph of y = f(x + 3) The coordinates of point A are (9, 1) Find the coordinates of point P. Q4. The graph of y = f(x) is shown on the grid. Sketch the graph of y = f( x) Q5. The graph of y = f(x) is shown on the grid. The graph G is a translation of the graph of y = f(x). Write down the equation of graph G.

3 Q6. The diagram shows a swimming pool in the shape of a prism. The swimming pool is empty. The swimming pool is filled with water at a constant rate of 50 litres per minute. Here are four graphs. Write down the letter of the graph that best shows how the depth of the water in the pool above the line MN changes with time as the pool is filled.

4 Q7. The graph shows information about the velocity, v m/s, of a parachutist t seconds after leaving a plane. Work out an estimate for the acceleration of the parachutist at t = 6 Q8. Using the graph in question 7, work out an estimate for the distance fallen by the parachutist in the first 12 seconds after leaving the plane. Use 3 strips of equal width.

5 Q9. Louis and Robert are investigating the growth in the population of a type of bacteria. They have two flasks A and B. At the start of day 1, there are 1000 bacteria in flask A. The population of bacteria grows exponentially at the rate of 50% per day. The population of bacteria in flask A at the start of the 10th day is k times the population of bacteria in flask A at the start of the 6th day. Find the value of k. Q10. Louis and Robert are investigating the growth in the population of a type of bacteria. They have two flasks A and B. At the start of day 1, there are 1000 bacteria in flask A. The population of bacteria grows exponentially at the rate of 50% per day. At the start of day 1 there are 1000 bacteria in flask B. The population of bacteria in flask B grows exponentially at the rate of 30% per day. Sketch a graph to compare the size of the population of bacteria in flask A and in flask B.

6 Topics listed in objectives Recognise, sketch and interpret graphs of the reciprocal function State the value of x for which the equation is not defined; y 1 with x 0 Recognise, sketch and interpret graphs of exponential functions y = k x for positive values of k and integer values of x; Use calculators to explore exponential growth and decay; Set up, solve and interpret the answers in growth and decay problems; Interpret and analyse transformations of graphs of functions and write the functions algebraically, e.g. write the equation of f(x) + a, or f(x a): apply to the graph of y = f(x) the transformations y = f(x), y = f( x) for linear, quadratic, cubic functions; apply to the graph of y = f(x) the transformations y = f(x) + a, y = f(x + a) for linear, quadratic, cubic functions; Estimate area under a quadratic or other graph by dividing it into trapezia; Interpret the gradient of linear or non-linear graphs, and estimate the gradient of a quadratic or non-linear graph at a given point by sketching the tangent and finding its gradient; Interpret the gradient of non-linear graph in curved distance time and velocity time graphs: for a non-linear distance time graph, estimate the speed at one point in time, from the tangent, and the average speed over several seconds by finding the gradient of the chord; for a non-linear velocity time graph, estimate the acceleration at one point in time, from the tangent, and the average acceleration over several seconds by finding the gradient of the chord; Interpret the gradient of a linear or non-linear graph in financial contexts; Interpret the area under a linear or non-linear graph in real-life contexts; Interpret the rate of change of graphs of containers filling and emptying; Interpret the rate of change of unit price in price graphs. x

7 Answers Q1. (0.5, 12), (3, 2), (5, 1.2) Q2. Q3. (6, 1) Q4. Parabola passing through (0, 4), (2, 0), (4, 4) Q5. y = f(x 6) Q6. C Q7. 3 to 4 m/s 2 (tangent at t = 6) Q m Q9. k = = Q10.